Abstract
We construct simple 3-designs and 4-designs of block-size 6 in the classical projective planesPG(2,q),q a power of 2. All of our designs are invariant under the projective groupPGL(3,q). Aside from several infinite series of 3-designs we get some relatively small designs of independent interest, e.g. designs with parameters 4-(21, 6, 16) and 4-(73, 6, 330) defined in the planes of orders 4 and 8, respectively.
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Bierbrauer, J. Designs with block-size 6 in projective planes of characteristic 2. Graphs and Combinatorics 8, 207–224 (1992). https://doi.org/10.1007/BF02349958
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DOI: https://doi.org/10.1007/BF02349958